When radio signals are being transmitted between a transmitter and a receiver, various interference influences occur which have to be taken into account during the receiver-end signal detection. Firstly, the signal is subject to distortion which is caused by there generally being two or more possible signal propagation paths. Owing to reflection, scatter and diffraction of signal waves on obstructions, such as buildings, mountains and the like, the reception field strength at the receiver is composed of a number of signal components, which generally have different strengths and different delays. This phenomenon, which is referred to as multipath propagation, causes the distortion of the transmitted data signal that is known as intersymbol interference (ISI).
Other active subscribers represent a further cause of interference. The interference that is caused by these subscribers is referred to as multiple access interference (MAI). One scenario that occurs frequently actually involves a dominant interference source or interference channel having a serious adverse effect on the signal detection in the user channel.
First of all, only one channel will be considered, that is to say MAI will be ignored. This multipath transmission channel between the transmitter S and the receiver E can be modeled as a transmission filter H with channel coefficients hk, as is illustrated in FIG. 1. The transmitter S feeds transmission symbols sk into the transmission channel, that is to say the channel model transmission filter H. An additive noise contribution nk can be taken into account by means of a model adder SU, and is added to the transmission symbols sk (filtered by means of hk) at the output of the channel model transmission filter H.
The index k denotes the discrete time in time units of the symbol clock rate. The transmission signals sk which have been filtered by means of the transmission filter H and on which noise is superimposed are received as the received signal xk by the receiver E, such that:
                              x          k                =                                            ∑                              i                =                0                            L                        ⁢                                                  ⁢                                          h                i                            ⁢                              s                                  k                  -                  i                                                              +                      n            k                                              (        1        )            where L represents the order of the transmission channel that is modeled by the filter H. As can be seen from equation 1, ISI is present since xk depends not only on sk but also on sk−1, . . . , sk−L.
FIG. 2 shows the channel model transmission filter H. The filter H comprises a shift register comprising L memory cells Z. Taps (a total of L+1) are in each case located before and behind each memory cell Z and lead to multipliers which multiply the values of the symbols sk, sk−1, . . . , sk−L (which have been inserted into the shift register via an input IN at the symbol clock rate T−1) by the corresponding channel impulse responses h0, h1, . . . , hL. An output stage AD of the filter H adds the outputs from the L+1 multipliers. This thus results in an output signal OUT corresponding to equation 1.
The state of the channel is described by the memory contents of the channel model shift register. The memory contents of the first memory cell on the input side contain the symbol sk−1 (which is multiplied by h1) in the time unit k, and the further memory cells Z are filled with the symbols sk−2, sk−3, . . . , sk−L. The state of the channel in the time unit k is thus determined uniquely by the details of the memory contents, that is to say by the L-tuple (sk−L, sk−L+1, . . . , sk−1).
In the receiver E, the received signal values xk are known as sample values, and the channel impulse responses h0, h1, . . . , hL of the channel are estimated at regular time intervals. The object of the equalization process is to calculate the transmission symbols sk from this information. Equalization by means of a Viterbi equalizer will be considered in the following text.
Viterbi equalization is based on finding the shortest path through a state diagram of the channel, which is known as a trellis diagram. The channel states are plotted against the discrete time k in the trellis diagram. According to the Viterbi algorithm (VA), a branch metric is calculated for each possible transition between two states (previous state relating to the time unit k→target state relating to the time unit k+1), and represents a measure of the probability of that transition. The branch metrics are then added to the respective state metrics (also frequently referred to as path metrics in the literature) of the previous states. In the case of transitions to the same final state, the sums obtained in this way are compared. That transition to the final state in question whose sum of the branch metric and the state metric of the previous state is a minimum is selected and forms the extension of the path leading to this previous state to the target state. These three fundamental VA operations are known as ACS (ADD-COMPARE-SELECT) operations.
Now, from the combinational point of view, the number of paths through the trellis diagram increases exponentially as k rises (that is to say as time passes), it remains constant for the VA. The reason for this is the selection step (SELECT). Only the selected path (the survivor) survives and can be continued. The other possible paths are rejected. Recursive path rejection is the core concept of the VA and is an essential precondition for the use of computation to solve the problem of searching for the shortest path (also referred to as the “best path”) through the trellis diagram.
The number of channel states (that is to say the number of possible ways in which the shift register H may be occupied) in the trellis diagram, which is identical to the number of paths followed through the trellis diagram, is mL. In this case, m denotes the significance of the data symbols being considered. The computation complexity of the VA accordingly increases exponentially with L. Since L should correspond to the length of the channel memory of the physical propagation channel, the complexity for processing the trellis diagram increases as the channel memory of the physical propagation channel rises.
One simple method to reduce the computation complexity is to base the trellis processing on a short channel memory L of, for example, three or four time units (taps). However, this has a severe adverse effect on the performance of the equalizer. A considerably more sensible measure for limiting the computation complexity, which does not have a serious influence on the quality of the equalizer, is the decision feedback (DF) method. In the case of the DF method, the VA is based on a reduced trellis diagram, that is to say a trellis diagram in which only some of the mL channel states are considered rather than all of them. If the trellis diagram is reduced to mLDF trellis states (LDF<L), the remaining L-LDF channel coefficients (which are not used for the definition of trellis states) are still taken into account by being used for the calculation of the branch metrics in the reduced trellis diagram.
A branch metric must be calculated for each possible transition between two states both during the processing of the complete trellis diagram and during the processing of the reduced trellis diagram (DF case). The branch metric is the Euclidean distance between the measured signal value or sample value xk and a reconstructed “hypothetical” signal value which is calculated and “tested” with respect to the target state, the transition from the previous state to the target state and the path history, taking into account the channel knowledge in the receiver:
By way of example, let us assume that m=2 (a binary data signal), that is to say there are 2L (DF case: 2LDF) trellis states (0, 0, . . . , 0), (1, 0, . . . , 0) to (1, 1, . . . , 1) comprising L tuples (DF: LDF tuples). One specific hypothetical previous state is assumed to be defined by the shift register occupancy (aL, aL−1, . . . , a1) (in the DF case, only the LDF right-hand bits (aLDF, . . . , a1) of the shift register occupancy are used for the state definition). The hypothetically transmitted symbol (bit) 0 or 1 is denoted by a0, and changes the previous state (aL, aL−1, . . . , a1) in the time step k to the target state (aL−1, aL−2, . . . , a0) in the time step k+1 (DF: previous state (aLDF, . . . , a1) to the target state (aLDF−1, . . . , a0). The branch metric BMk, with or without DF, is:
                                                                        BM                k                            =                            ⁢                                                                                                            sample                      ⁢                                                                                          ⁢                      value                                        -                                          reconstructed                      ⁢                                                                                          ⁢                      signal                      ⁢                                                                                          ⁢                      value                                                                                        2                                                                                        =                            ⁢                                                                                                                                                                  x                          k                                                -                                                  (                                                                                                                    ∑                                                                  i                                  =                                  1                                                                L                                                            ⁢                                                                                                                          ⁢                                                                                                h                                  i                                                                ⁡                                                                  (                                                                      1                                    -                                                                          2                                      ·                                                                              a                                        i                                                                                                                                              )                                                                                                                      +                                                                                          h                                0                                                            ⁡                                                              (                                                                  1                                  -                                                                      2                                    ·                                                                          a                                      0                                                                                                                                      )                                                                                                              )                                                                                                            2                                    ⁢                                                                          ⁢                  for                  ⁢                                                                          ⁢                                      a                    i                                                  =                                  {                                      0                    ,                    1                                    }                                                                                        (        2        )            
The reconstructed signal value (also referred to in the following text as the reconstructed symbol) is a sum of products of a channel coefficient and a symbol. For the DF case, the term
      ∑          i      =      1        L    ⁢          ⁢            h      i        ⁡          (              1        -                  2          ·                      a            i                              )      may also be split into a trellis contribution and a DF contribution:
                              BM          k                =                                                                        x                k                            -                              (                                                                                                    ∑                                                  i                          =                                                                                    L                              pr                                                        +                            1                                                                          L                                            ⁢                                                                                          ⁢                                                                        h                          i                                                ⁡                                                  (                                                      1                            -                                                          2                              ·                                                              a                                i                                                                                                              )                                                                                                            ︸                                              DF                        ⁢                                                                                                  ⁢                        contribution                                                                              +                                                                                    ∑                                                  i                          =                          1                                                                          L                          pr                                                                    ⁢                                                                                          ⁢                                                                        h                          i                                                ⁡                                                  (                                                      1                            -                                                          2                              ·                                                              a                                i                                                                                                              )                                                                                                            ︸                                              trellis                        ⁢                                                                                                  ⁢                        contribution                                                                              +                                                                                    h                        0                                            ⁡                                              (                                                  1                          -                                                      2                            ·                                                          a                              0                                                                                                      )                                                                                    ︸                                                                        hypothetical                          ⁢                                                                                                          ⁢                          symbol                                                contribution                                                                                            )                                                          2                                    (        3        )            
This means that the reconstructed symbol comprises two (DF case: three) contributions: a contribution which is governed by the hypothetically transmitted symbol a0 for the transition from the time unit k to the time unit k+1, the trellis contribution, which is given by the previous state relating to the time unit k in the trellis diagram, and, in the DF case, the DF contribution as well, owing to the reduced trellis states.
The branch metric BMk is always the same, with or without DF. As already mentioned, the computation saving in the case of the VA with DF results from the smaller number 2LDF of trellis states to be taken into account during the processing of the trellis diagram, that is to say the reduction in the trellis diagram.
If it is also intended to take into account an interference channel (that is to say a second multipath transmission channel) in the equalization of a data signal, joint VA equalization must be carried out for the two channels (the user channel and the interference channel). This is done by forming an overall trellis diagram which includes the states of both channels: one example, if m=2 (binary data signal) and L=4 for both channels, the trellis diagram for the user channel comprises 16 states, and the trellis diagram for the interference channel likewise comprises 16 states. The “combinational” overall trellis diagram on which the joint VA equalization of the two signals is based then comprises 16×16=256 states. If one additional DF bit is in each case taken into account (that is to say L=5, LDF=4), the overall trellis diagram still comprises 256 states, but another two DF bits are added as the DF contribution to the calculation of the branch metrics.
The complexity for processing the overall trellis diagram is increased by a factor of 16 in comparison to the complexity for processing the trellis diagram for the user channel.